Question

n趋于无穷大，1/(1*3)+1/(3*5)+…+1/[(2n-1)(2n+1)]极限

Answer 1

解：因为1/[(2n-1)(2n+1)]=(1/2)[1/(2n-1)-1/(2n+1)],
所以，原式=lim(1/2)[1-1/3+1/3-1/5+…+1/(2n-1)-1/(2n+1)]
n趋于无穷大
=lim(1/2)[1-1/(2n+1)]
n趋于无穷大
=1/2